Analysis of Tissue Fluorescence

8/9/2019 Analysis of Tissue Fluorescence

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V. Gavryushin

Institute of Materials Science and Applied Research and Semiconductor Physics department, Vilnius

University, Vilnius, Lithuania. E-mail: [email protected]

Abstract:

The aim of this article is to present a developed method that decomposes the autofluorescencespectrum into the spectra of naturally occurring biochemical components of biotissue. It requiresknowledge of detailed spectrum behaviour of different endogenous fluorophores. We have studiedthe main bio-markers in human tissue and proposed a simple modelling algorithm for their spectrashapes. The empirical method was tested theoretically by quantum-mechanical calculations of thespectra in the unharmonic Morse potential approach.

Key Words : spectroscopy, biotissue, fluorescence, autofluorescence, fluorophores, Morse potential,quantum calculations

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Now is abundantly clear that the developments of laser use in the therapy and diagnostics

(e.g., photodynamic therapy, optical tomography, 3D-microscopy, etc.) had been achieved. There

has been increasing interest recently in the field of fluorescence-based techniques for thecharacterization of human lesions in clinical oncology. Several groups are developed

fluorescence spectroscopy for early detection of the premalignant lesions [1- 9].

Fluorescence spectrum of the tissue may be attributed primarily to the superposition of the

fluorescence from a variety of interacting biological molecules, some of them as the naturally

occurring fluorophores. We suggest that spectra decomposition to its constituents has to be done

first [1, 2], as is usual in the molecular spectroscopy, then followed by statistical analysis of

decomposed elements or the whole spectra to find any correlation with medical indications of

the biomedical object under study [ 2,3,4].

The question, then, arises: which of fluorescent chemical components one has to consider

for the reconstruction of fluorescent spectra and how much of each has to be included for a

perfect fit to overall fluorescence. In addition to that, it is well known, that the fluorescence

emission line-shapes of macromolecules are strongly asymmetric. Therefore one might want to

have a good enough model approximating the line shapes of the fluorophores. This is an issue I

am addressing in this paper.

mailto:[email protected]:[email protected]


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We have studied here the technique of resolving the total fluorescence spectra of tissue into

the main fluorescent components by curve fitting [2]. A spectra resolution as a set of overlapping

endogenous lines was carried out for better understanding of biochemical changes in normal and

malignant biomedical samples [5]. For data evaluation and reconstruction of the line shapes of

the studied fluorophores an empirical asymmetric-Gaussian-model, firstly used in [2], was

introduced.

Since empirical method needs to be tested theoretically, a quantum calculation of the

molecular emission spectra was done in an unharmonic Morse potential approach in the discreet

variable representation [10]. Having done this, one could compare both the calculated and

empirical spectra. It was found that the simple approach of "truncated Gaussian" goes in good

agreement with measured asymmetric fluorescence spectral shapes and therefore is good enough

to use as an approximation for it.

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Pulsed laser-induced-fluorescence studies of pathologically certified tissues of premalignant

and benign lesions in the female genital tract (uterus glandular cervical squamous epithelium)

were carried out, as described in more detail in Ref. [2]. Laser induced autofluorescence (AF)

measurements in vitro were performed with pulsed laser (3rd harmonic of Nd +3-glass laser: wexc

= 3,51 eV, 70 ns of pulse duration, 1Hz - repetition rate) as excitation source [2]. Tissue

fluorescence spectra were measured by a "time-gated" (registration gate of 5 ns width and 10 ns

delay after an excitation pulse) computer controlled, hand-made spectrophotometer [2]. Sixty

patients were included in the study. For every tissue sample, three measurements (in different

locations) were carried out. Spectra were used only from samples certified by histopathology

analysis as normal/malignant. The conditions of excitation and of the collection of emission light

were the same for all measurements. Laser light was focused ( » 1 mm 2) to the sample pressed

between two quartz plates.

The normalized experimental autofluorescence spectra of all tested tissue samples of

different levels of pathology are shown in Figure 1a, and demonstrates the variations of the

spectra of a same tissue type from one patient to another. Spectral data set was evaluated by

MathCAD data processing software were written script, analyses every spectrum as the

composition of the same set of asymmetric components. The used spectral components

correspond to the known fluorophores [1,2, 9,11].


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bb ))

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a) The set of the normalized autofluorescence spectra of the measured tissue samples of differentlevels of pathology, - from hyperplasia to cancer.

b) Fluorescence spectra of the main used endogenous fluorophores constructed by model (1)-(3):Collagen (395 nm), elastin (415 nm), NADH (453nm), unidentified (483 nm), caroten (525nm),

porphyrins (HDP 608 & 678nm). Biomarker’s spectra were derived from an experimental spectra(a). The spectral components, derived by multivariate curve resolution (Figure 2b), are shown by thinlines for comparison.

The intensity of emission of tested tissues had a large variation (about 2 orders) from patient

to patient, also for tissues of the same patient, but for different excitation places. The spectral

shape also display a large variation (Figure 1a), but more differ from patient to patient.


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basis spectra parts responsible for the spectral variation [3,4]. Derived principal components

were tested with the Malinowski’s indicator function [13] to select statistically significant

principal components (factors). In Figure 2a, some principal components are shown. Remaining

principal components describes only noise (8th and further, Figure 2a) and they are discarded

from further analysis. Only seven factors were found to be statistically significant.

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The comparison of averaged fluorescence spectra of samples from different histology groups (solidline) with the full average spectrum of all samples (broken line) [2]. Dotted lines show the maincomponents forming the spectra (from right to left): HDP (678 nm); HDP (608 nm); flavin-caroten(525 nm); unidentified (483 nm); NADH (453 nm); neopterin (430 nm, darkened); elastin (415 nm);collagen (395 nm). On the top, - the difference spectra between averaged spectra of desease groups(solid) and full averaged spectrum (broken) are shown.

However, this factors are not yet directly related to any real chemical spectra (some of them,

for example, are negative, Figure 2a). Non-oblique factor rotation transforms them to physically

meaningful spectral profiles, then, alternating least squares MatLab’s algorithm optimized the

recovered profiles (Figure 2b) [4]. The factors, were used as initial estimates and non-negativity,

unimodality and linear additivity of spectra, were assumed as chemical constraints. In Figure 2b,

resolved spectral profiles by multivariate curve resolution are shown. Resolved spectra can be

compared to known fluorophores spectra (Figure 1b) used in our previous work [2]. Obtained

pure spectra can be used to identify chemical species using library spectra [6].

The evaluation of experimental spectra shows that autofluorescence requires at least 7

components to be fully accounted for all spectral changes [3]. Figure 1b shows the fluorescence


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spectra of used endogenous fluorophores as biomarkers for the spectral analysis. The known data

for endogenous fluorophores are quite different [1,9]. Data evaluation [2,11] was made, firstly,

by reconstruction of the biotissue spectra as the sum of the same set of line-shapes of

endogenous fluorophores (Figure 1b): collagen, elastin, carotene, neopterin [11], NADH, FAD

(nicotinamide and flavin adenine dinucleotides), porphyrins [14-18]. Further, an analysis was

based on the difference of the tissue spectra from an averaged spectrum of healthy tissues.

Endometrial tissues samples were biopsied, classified by routine histopathology, and

grouped as Normal, Hyperplastic (HP) or Cancerous (CN). This samples categories of different

diagnosis were analyzed [2,3,11]. Mean-scaling was performed by calculating the mean

spectrum (broken line spectra in Figure 3) for all more healthy patients and subtracting it from

each patient spectrum and from an averaged spectra for patients grouped by same diagnosis.

However, unlike normalization, mean-scaling displays the differences (dashed spectra on the topof Figure 3) in autofluorescence spectra with respect to the artificial healthy tissue averaged

spectrum. Therefore, this method maximally enhances the differences in autofluorescence

spectra between tissue categories when spectra are acquired from non-diseased and diseased

sites from each patient. As an example of aforementioned spectra-processing, results are shown

in Figure 3 [2, 3]. A difference factors between averaged spectra of the groups (solid lines) and

the healthy tissue averaged spectrum (broken lines) are shown on the top of the each spectrum.

As we can see, the neopterin presence in cancer (b) and polyp (c) stages of the tissue is abouttwice more evident, and more, has opposite changes comparing to hyperplasia (a). Opposite

changes in the difference factor stand for enhancement of its presence, in relationship to the

mean composition, while in hyperplastic case (a), its presence is weakened [ 2,11 ].

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For the reconstruction of the spectra of fluorophores, as bio-markers, the normalized line-

shape function S i( w) can be calculated as an asymmetric-Gaussian [2, 11 ]:

)(D)(G)(

1)( cui5

1 0

w w w

w hhh

hit

i

iS

S ×=ò×

, (1)

]exp[1

)(G2

0i ÷÷ ø

öççè

æ D-

-D

=ii

i E w

p w

hh , (2)

]exp[)(D0

i

i

ii

ii

icut

E g

÷÷ ø

öççè

æ D

D---= g

g w

w

hh

. (3)

Here G i( w) is an usual symmetrical Gaussian function of a half-width Di and the maxima energy


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E0; D Cut( w) is a cutting factor-function (of a g -rank) deforming the initial Gaussian; g is a width

factor of the cutting function; ò×5

1 0)( w hS =0.445 is the integral, normalizing spectral function

Si( w) area to 1. Rather like attempts for the molecular line-shape approximations can be foundalso in [19,20].

FF iigguu rr ee 44

a) Reconstruction procedure of measured neopterin spectrum

(points) by the proposed line-shape (1). The calculated spectrum

Si( w) plot is filled, solid line is the Gaussian function G i( w),dotted line is the cutting function D Cut( w), deforming the

Gaussian. Parameters: l 0=429.2 nm; D = 0.38 eV; g =1; g = 4.

b) The typical spectral shapes of other bio-markers, as collagen,

elastin, NADH, and b-carotene are shown also under the samemodeling.

As an example, such reconstruction of our measured [ 8,11 ] spectrum of a neopterin (points)

together with factorizing components (2) and (3) are shown on Figure 4. We show also the

spectrum (by broken line over points) obtained from the below following quantum calculations

(same as one in Figure 7) . The good correspondence between experimental, empirical and calculated


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below spectra allow us to state that a simple asymmetric-Gaussian model (1) - (3) as line-shape

approximation is good enough to be used for real spectral analysis. Usually it is enough to

change only two parameters in (1) - (3): the spectral position l 0 and the spectral width Di.Therefore, we have the simple 2-parameter approximation for the tabulation of the spectral

components as bio-markers. The typical spectral shapes of other biomarkers, such as collagen,

elastin, NADH, and carotene are also modeled similarly and are shown in Figure 4b. It is

noteworthy that all spectral components in Figure 1b and Figure 3 were calculated also by

proposed model.

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Morse potentials and some of the calculated eigenstates and wavefunctions for the ground g andexcited e molecular states. Arrows show the transitions for light emission and absoption.

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For theoretical arguments of above simple spectra modeling, we carried out the quantum

calculations of stationary Schr ! dinger equation in an unharmonic Morse potential approach. The


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vibrational wavefunctions were obtained within discrete variable representation (DVR) method

[21]. The DVR is a grid-point representation in which the matrix elements of the potential

energy operator V(r) is approximated as diagonal and the kinetic energy as a sum of one-

dimensional matrices [22, 23]. The formalism is permitting the line shape calculations starting

only from a given interaction potential. Some of the calculated wavefunctions and eigenvalues

are shown in Figure 5. We have calculated the spectra for emission and absorption (Figure 7) and

compared them with an empirical approximation (1) presented above.

FF iigguu rr ee 66

Potential curves and some of the calculated wavefunctions for the ground g and excited e molecularstates calculated for some value of Franck-Condon (FC) shift. Arrows - light emission transitions.

Morse potential approximation

The Morse potential is actually a good representation for the molecular potential energy and

gives as the asymmetrically shaped emission and absorption lines. The Morse potential is

2)( )1()( e R Re e D RV ---= b ,

ee D

mpn b

2= (4)


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ve is the vibrational constant and µ is the reduced mass of molecule. Repulsive forces make the

potential steeper than parabolic when the bond length is compressed and less steep when the

bond length is expanded (Figure 5).

Schr dinger Equation solution in Discreet Variable Representation (DVR)

We select DVR method [24, 25] for our MathCAD calculations since it avoid having to

evaluate integrals in order to obtain the Hamiltonian matrix and since an energy truncation

procedure allows the DVR grid points to be adapted naturally to the shape of any given potential

energy surface. The primary feature is that DVR gives an extremely simple kinetic energy matrix

m2$ 2,2

, k ik i k T h= with conditional formulation:

úû

ù

êë

é

--¹=

-

3,

)(

)1(2,

2

2,

p g

k i g k iif T

k i

k i

) (5)

We use the energetically weighted grid parameter g depending on a number of calculus points

imin:

22 12

÷ ø öç

è æ =

dr g

m

h

min

minmax

ir r

dr -= (6)

Here r max and r min defines the range variables for the bond length r. The diagonal matrix of the

potential energy k iV , )

for Morse potential (4) is as:

),,0,(, ik i V elsek iif V ¹= )

(7)

Then matrix for the full Hamiltonian (in Hartrees) will be:

k ik ik i V T H ,,,$$$ += (8)

The eigenvalues (stationary states) as the solutions of the Schr ! dinger equation

)()($ r E r H ii y y = then are sorted:

))$(( H eigenvals sort e = . (9)

Wavefunctions for every of eigenvalues n= 0,..,99 are got by simple MathCAD procedure:

),$( nn e H eigenvec=y . (10)

Finally, wavefunctions was normalized in atomic units:

N

y y = , ú

û

ùêë

é=

åin

in

i dr a

N y y 0

1. (11)

Some of calculated wavefunctions and energy states are shown in Figure 5. An important feature


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is the increase of density of states of the vibrational energy levels with larger quantum number.

The states over the dissociation energy D g are unbound and delocalized as you can see for the

state v g=99 in Figure 5. Moreover, it is seen that in some cases the emission from an excited

state can be quenched resonantly by unbound ground states.

Electronic Transitions and Franck-Condon Factors

The emission and absorption spectra of molecules was defined by the dipole matrix

elements of optical transitions as the integrals á || ñ over the vibrational coordinates:

init vibr

final vibr

init electr

final electr

init vibr el

final vibr el YY´YY=YY |$$ .. mm , (12)

which has the form of the dipole integral of electronic transitions multiplied by the "overlap

integral" between the initial and final vibrational wavefunctions (Figure 6). It is clear that, due to

the asymmetry of molecular potentials, the emission spectra will be wider than the absorption

spectra.

The squares of overlap integrals init vibr final vibr YY | inside the transition rate expression are

called as "Franck-Condon factors" (FCF). Their magnitude plays the main role determining the

relative intensities of vibrational "bands" within a particular spectrum of electronic transitions.

Therefore, FCF determines the shapes of spectral lines. The overlap of wavefunctions (Figure 6)

in forms ág0|eiñ and áe0|giñ, determining the absorption and emission probabilities, are calculatedand their spectra are shown in Figure 7 for different values of the shifts of potential minima:

d r = R e-R g . If the difference in potential curves minima d r is growing then the spectra became

wider.

Fluorescence spectra of bio-molecules, as have been shown on simple quantum-theoretical

background, are of asymmetric profiles. One of the spectra from Figure 7 is drawn on Figure 4

(broken line over points) over the measured neopterin spectrum (points). The good agreement

between quantum-calculated, measured, and empirical approximated (1) spectra are evident.


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FF iigguu rr ee 77

Fluorescence and absorption spectra calculated in Morse potential approach for different values ofFranck-Condon shift” d r (%).

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A method was discussed for the biotissue autofluorescence spectra decomposition into its

constituent’s fluorescence spectra. The decomposed spectra correspond to naturally, within the

object occurring fluorescent substances which, if its concentrations correlate with medical

indications, serves as a biomarker for disease diagnostics.

Fluorescence line-shape, on its own, was shown to be explained by two-parameter-only

asymmetric-Gaussian model. To prove this, a quantum calculation of molecular emission spectra

using Morse potential approach was employed. The comparison of the both calculated and

empirical spectra with experimental one shows that simple spectra modeling [2,11] is useful for

the description of the biomedical object spectra.

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The author wish to thank colleagues E. Auksorius for his skilled support and data statistical

treatments and MD. A. Vaitkuviene for the expert support on medicine aspects.


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Analysis of Tissue Fluorescence